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Lie Theory
V. K. Agrawala and Johan G. Belinfante; Weight diagrams for Lie group representations:
A computer implementation of Freudenthal's algorithm in ALGOL and FORTRAN,
BIT (1969) 9(4):301-314,
doi: 10.1007/BF01935862
John C. Baez; The octonions,
Bull. Amer. Math. Soc. (2002), 39:145-205,
doi: 10.1090/S0273-0979-01-00934-X
Arjeh M. Cohen and Willem A. de Graaf;
Lie algebraic computation,
Com. Phys. Comm (1996) 97:53-62,
doi: 10.1016/0010-4655(96)00021-5
Arjeh M. Cohen et al.;
Computing in groups of Lie type,
Math. Comp. (2004) 73:1477-1498,
doi: 10.1090/S0025-5718-03-01582-5
E. de Sousa Bernardes;
Killing - An algebraic computational package for Lie algebras,
Computer Physics Communications (2000) 130(1-2):137-175,
doi: 10.1016/S0010-4655(00)00006-0
Peter B. Gilkey;
Some representations of exceptional Lie algebras,
Geometricae Dedicata (1988) 25(1-3):407-416,
doi: 10.1007/BF00191935
V. M. Gordienko;
Matrix entries of real representations of the group O(3) and SO(3),
Siberian Mathematical Journal (2002), 43(1):36-46,
doi: 10.1023/A:1013816403253
Roger Howe;
Very Basic Lie Theory,
The American Mathematical Monthly (1983), 90(9):600-623
Correction in: (1984) 91:247
R. B. Howlett, L. J. Rylands and D. E. Taylor;
Matrix generators for exceptional groups of Lie type,
J. Symbolic Computation (2001) 31(4):429-445,
doi: 10.1006/jsco.2000.0431
G. Itzkowitz, S. Rothman and H. Strassberg;
A note on the real representation of SU(2,C),
Journal of Pure and Applied Algebra (1991), 69(3):285-294,
doi: 10.1016/0022-4049(91)90023-U
D. Rand, P. Winternitz and H. Zassenhaus;
On the identification of a Lie algebra given by its
structure constants. I. Direct decompositions, Levi decompositions,
and nilradicals,
Linear Algebra and its Applications (1988), 109:197-246,
doi: 10.1016/0024-3795(88)90210-8
L. J. Rylands and D.E. Taylor;
Matrix generators for the orthogonal groups,
J. Symbolic Computation (1998) 25(3):351-360,
doi: 10.1006/jsco.1997.0180
Aaron Wangberg and Tevian Dray;
Visualizing Lie subalgebras using root and weight diagrams,
Loci (February 2009),
doi: 10.4169/loci003287
Johan G. F. Belinfante, Bernard Kolman;
A survey of Lie groups and Lie algebras with applications and computational methods,
SIAM, 1989,
ISBN-0898712432
Manfred Böhm;
Lie-Gruppen und Lie-Algebren in der Physik:
Eine Einführung in die Mathematischen Grundlagen,
Springer, 2011,
ISBN-3642203787
Robert N. Cahn;
Semi-simple Lie algebras and their representations,
Dover, 2006,
ISBN-0486449998
Roger W. Carter;
Simple groups of Lie type,
Wiley, 1972,
ISBN-0471137359
Nathan C. Carter;
Visual group theory,
The Mathematical Association of America, 2009,
ISBN-088385757X
Marvin Chester;
Primer of quantum mechanics,
Dover, 2003,
ISBN-0486428788
J. P. Elliott, P. G. Dawber;
Symmetry in physics,
Volume 1: Principles and simple applications
Volume 2: Further applications,
Macmillan, 1979,
ISBN-0333382722
Willem A. de Graaf;
Lie algebras: Theory and Applications,
North-Holland, 2000,
ISBN-0444501169
Jürgen Fuchs, Christoph Schweigert;
Symmetries, Lie algebras and representations
Cambridge University Press, 1994,
ISBN-0521560012
Howard Georgi;
Lie algebras in particle physics,
Westview Press, 1999,
ISBN-0738202339
Robert Gilmore;
Lie groups, physics and geometry,
Cambridge University Press, 2008,
ISBN-9780521884006
Willem A. De Graaf;
Lie algebras, Theory and algorithms,
North Holland, 2000,
ISBN-0444501169
James E. Humphreys;
Introduction to Lie algebras and representation theory,
Springer, 1973,
ISBN-0387900535
Nathan Jacobson;
Lie algebras,
Courier Dover Publications, 1979,
ISBN-0486638324
Hugh F. Jones;
Group theory and physics,
IOP Publishing, 1990,
ISBN-0852740301
Harry J. Lipkin;
Lie Groups for Pedestrians,
Courier Dover Publications, 2002,
ISBN-0486421856
R. Mirmin;
Group theory: An intuitive approach,
World Scientific, 1995,
ISBN-9810233655
Shlomo Sternberg;
Group theory and physics,
Cambridge University Press, 1994,
ISBN-0521558859
John Stillwell;
Naive Lie theory,
Springer, 2008,
ISBN-9780387782140
Kristopher Tapp;
Matrix groups for undergraduates,
American Mathematical Society, 2005,
ISBN-0821837850
V. S. Varadarajan;
Lie groups, Lie algebras and their representations,
Springer, 1984,
ISBN-0387909699
Brian G. Wybourne;
Classical Groups for physicists,
Wiley, 1974,
ISBN-0471965057
R. J. Riebeek;
Computations in Association Schemes,
PhD dissertation (1998),
Technical University Eindhoven, Netherlands,
available
online (accessed June 2014)
Home page
of Prof. John Baez at UC Riverside (see, e.g.,
this page)
Atlas of Lie groups and representations
LieTools
are a set of MATLAB tools attempting to visualize
structure constants of classical and exceptional Lie algebras.
My semi-simple-minded thoughts
on the visualization of Lie theory concepts
Title: A note on random samples of Lie algebras
(arXiv:1407.3642)
Abstract: Recently, Paiva and Teixeira
(arXiv:1108.4396)
showed that the structure constants of a Lie algebra
are the solution of a system of linear equations
provided a certain subset of the structure constants
are given a-priori.
Here it is noted that Lie algebras generated in this way
are solvable and
their derived subalgebras are Abelian
if the system of linear equations
considered by Paiva and Teixeira is not degenerate.
An efficient numerical algorithm
for the calculation of their structure constants
is described.
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